California World Class Math
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Learn About California Math Standards

    Open Process to Raise Standards

     An outcry over low student achievement led to the current California Math Standards.

     Math professors in the state college system noticed that over a ten year period, the remediation rate had more than doubled—over twice as many first year college students needed remedial math classes. During the same period, math programs used by many local schools did not teach traditional algorithms, provide daily practice or use a traditional textbook.  Additionally, high school graduation requirements were set by individual districts, and in many districts, Algebra was not required for high school graduation. The result was a two tier graduation status and a corresponding racial disparity: many high achieving students bound for college took high level math classes, and other students, predominantly minority, took general math classes that did not prepare them for college.

     The foregoing, along with very poor performance on national and international testing, motivated California educators, politicians and other community leaders to advocate for raising math standards for all students in the state.

     In nonpartisan fashion, the California legislature passed Education Code Section 60605 which required the State Board of Education to adopt new grade level content standards in mathematics.

     Educators and community leaders were appointed to an Academic Standards Commission that was charged with making recommendations to the State Board of Education. The Commission held open meetings and followed processes described by the State Board of Education. The State Board of Education also commissioned an Advisory Committee of internationally respected university mathematics professors.

     The State Board followed its open process, held open meetings, took testimony, and ultimately adopted the current California Math Standards in December 1997. The Math Standards have remained in effect for the past eleven years because they are sound, solid, high standards that permit California to educate all students at levels consistent with their counterparts around the world.

California Math Standards Are Internationally Competitive

     California’s Math Standards describe what to teach, not how to teach it. They are rigorous, comprehensive and specific. The standards provide solid benchmarks—stating explicitly what content and skills students should master at each grade level to remain on par with students from other nations.

     Before the standards were adopted, internationally respected university math professors on the State Board of Education’s Advisory Committee analyzed grade level math standards in countries with top math students by world standards. They modeled the benchmarks against the benchmarks in three countries:  Japan, Singapore, and Hungary.  Although these countries are culturally very different, they consistently produce top level mathematicians, engineers and scientists. Their top students test at the highest levels internationally, and some of their average students test like America’s top students.

     As a result of this investigation, the State Board of Education was able to adopt math standards that are internationally competitive and respected.

     Following the adoption in December 1997, the Fordham Foundation commissioned a detailed study of the math standards across forty-six states, the District of Columbia and Japan. California k-12 math standards received the highest rating along with Japan and one other state.  In 2006, there was another assessment of math standards commissioned by the Fordham Foundation, and again California received its highest ranking.  Numerous others have endorsed the California Math Standards.

California Math Standards Are College Preparatory

     By adopting state-wide rigorous math standards California sought to even the playing field for all students—regardless of their ethnicity, race or wealth. By teaching and testing to the standards, school districts give students an opportunity to master grade level content and skills. This gives students from all walks of life an opportunity to succeed in higher education.

Framework Describes Instructional Strategies

     The California Math Framework is a separate document from the Math Standards. The Framework addresses instructional strategies, materials and programs, professional development and assessments that align with the Math Standards. The Framework provides instructional guidance to teachers to enable them to help students achieve mastery of the standards. 

     The Framework identifies the "green dot standards," the key standards for each grade level.  These topics in the standards are the most important ones to master at each grade level.  They comprise 85% of the questions on the end of the year math exams.

     The Framework discusses and explains whereas the Math Standards set benchmarks. The Math Standards do not address instructional strategy or educational pedagogy.

    California educators with differing points of view on instruction can agree about end of the year benchmarks for all students while they differ on instructional strategies.

Effective Textbooks and Instructional Materials, including Chapter and Unit Tests Raise Academic Achievement

     California provides funds for textbooks, teachers’ manuals, tests, and other instructional materials. Following the state adoption of Math Standards in 1997, the Legislature set up a billion dollar textbook fund from 1998-2002 from which districts could purchase state adopted math textbooks that aligned with new state standards. The first adoption was in 1999, and since then there have been two additional adoptions and supplementary adoptions.

     Textbooks and other instructional materials go through a challenging public process before state adoption. The Curriculum Commission reviews submitted instructional materials and makes recommendations to the State Board of Education. But before it does so, two other panels review submitted materials. The Content Review Panel is composed of mathematicians who review submitted instructional materials for mathematical accuracy. Another panel, the IMAP, reviews submitted instructional materials for teachability, and at least fifty percent of the IMAP must be classroom teachers. After it receives reports from these two groups, the Curriculum Commission holds public hearings and then makes recommendations to the State Board of Education. After public review, the State Board votes on adoption.

     Instructional programs are evaluated based on five areas of review: alignment with the standards, program organization, assessments, universal access and instructional planning and support. Along with the above, they must demonstrate legal and social compliance.

     Only kindergarten through eighth grade mathematics instructional materials must go through the state adoption process. High School materials must be approved only insofar as they contain no cultural or other bias in the materials.

     The most recent adoption in 2007 invited publishers to submit math instructional materials under three categories: (1) Basic Grade Level, (2) Intervention, and (3) Algebra Readiness. Basic Grade level is a comprehensive program for each grade level providing at least fifty minutes of instruction per day. The programs must provide materials for students at, above and below grade level. The Intervention materials provide support for students who are two or more years below grade level. The Intervention programs provide intensive instruction and assume extended learning time.  An intervention program enables students to accelerate and reach grade level mastery.  The Algebra readiness program is intended for students who are not ready for Algebra 1. It assesses students’ weaknesses and focuses on addressing gaps in students’ knowledge and fluency to prepare them for an authentic Algebra course.

Math Standards Are Integrated Into State Accountability Scheme

     The adoption of rigorous math standards was one part of a nonpartisan movement to raise academic achievement in the state. Other parts include state-wide end of the year achievement testing, a school ranking system, requiring Algebra for graduation and a high school exit exam (CAHSEE).


     California Standards Tests assess whether students have mastered key grade level content and skills.  The state has released previously given math questions at each grade level, and these are available on the Department of Education website.  The state also provides a blueprint showing the what standards are tested on end of the year examinations.  The tests parallel the content and assessments in the state adopted math textbook series.

    Performance on California Standards Tests is graded into five performance levels.  Generally, about 70% correct on a test indicates grade level proficiency, and the state calls students who test at that level or above “Proficient.”  Students who do exceptionally well are identified as “Advanced.”  Students who fall below the Proficient cut off (below grade level expectations) are described as Basic, Below Basic and Far Below Basic.

     Prior to the development of the California Standards Tests which fully align with state standards, the state used nationally normed math achievement tests, the SAT9 and the CAT6. But once the California Standards Tests that align fully with state standards were developed, the state ceased its reliance on nationally normed tests, and has given them only to certain grade levels to link California’s student achievement with nationwide performance benchmarks.

    Academic Performance Index

     Academic Performance Index (API) is a number which ranks overall academic achievement in schools based on weighted averages of end of the year academic testing in all required subjects (mathematics and language arts for each year—science and social studies for select years).  The API is a number between 200-1000, with 800 indicating a high performing school.

    The state also gives each school a decile ranking.  This is a number between 1 and 10 indicating where the school’s API ranking falls compared to other schools in the state.  A decile ranking of 10 indicates that the school is in the top ten percent of all the schools in the state, a decile ranking of 1 indicates the bottom ten percent.

    Similar School Ranking

     Similar school ranking is the state’s way of letting schools know how they fare next to other schools with similar demographic characteristics.  The Similar School Ranking compares a school to the one hundred schools in the state with the most similar demographic characteristics, in areas such as student mobility, parent education, teacher education, percentage of low socioeconomic students, percentage of English learners, among other things.

    After identifying the 100 similar schools, the state ranks them by their API results, and then divides them into decile groupings.  Schools in the highest 10% of API will have a 10 as a Similar Schools Ranking.  Schools in the lowest 10% of API rankings compared to their 100 demographically similar schools receive a 1, the lowest ranking.

    Algebra and the High School Exit Examination (HSEE)

     California has made passing an Algebra class a high school graduation requirement. Prior to this requirement, there were two math tracks in many districts, one for students in “general math” who were not college bound, and another for students who began with Algebra and who were college bound. By making Algebra a high school graduation requirement, the state has leveled the field and given more students the opportunity to participate in higher education.

     The High School Exit Exam is now a requirement for graduation. A blueprint of the exam questions and sample questions are on the Department of Education website. Although the exam has Algebra questions on it, the cut scores are low enough so that a student can pass the test by correctly answering pre-algebra questions.

Statistics Indicate that More and More Students Are Excelling and Reaching Grade Level Standards

     When California adopted rigorous math standards in 1997, there was general approval from all segments of society, but there was also criticism among a small number of educators and others that the standards were too rigorous for the general population.

     In some instances, districts chose not to align with state standards but follow their own teachers’ views on what to teach at each grade level.  A few educators espoused that memorizing multiplication facts in the third grade was too demanding. Others complained about testing and argued that since Hispanic and other minority children were poor test takers, they should not have to take tests.  Some complained about traditional algorithms and argued that children should have the opportunity to create their own methods of long division and not learn the traditional algorithms. Complaints such as these have diminished over the years as educational outcomes have greatly improved.

     When math standards were established in December 1997, California began developing end of the year achievement tests that would directly align with the state math standards. Since state adopted math instructional materials, textbooks, tests, and supplementary materials also aligned with state math standards, an end of the year test that was aligned to state standards would evaluate whether students were actually learning the content and mastering the skills contained in the instructional materials and the standards.

     Because it would take several years to develop standards-based tests, California looked in the interim to private publishers of nationally normed achievement tests. From 1998 to 2001, beginning in the second grade, California schoolchildren took SAT9 math achievement tests published by the Harcourt Brace Company.

     A nationally normed test gives results in the form of a percentile ranking.  Before the test is available to the public, the publisher gives the test to several hundred thousand students.  It takes the results and plots them on a bell curve.  Generally, the raw scores that find their way into the mean and median (a band) are the 50th percentile.

     These types of tests are generally normed by different student demographic characteristics. There is a national norm of all the students who took the tests, an independent school norm for just private school students, a suburban norm for schools in suburban areas, and sometimes a parochial school norm for Catholic schools. Since national tests do not address a specific state’s standards, they have a range of very easy to difficult questions for each grade level.

     The rule of thumb is that the 50th percentile on a nationally normed end of the year math achievement test indicates grade level knowledge by national standards.

     The chart below taken from the California Department of Education website shows that after the state math standards were adopted, there was a significant increase in the percentage of students who tested above the 50th percentile. The percentage increase equates to thousands more students testing at the 50th percentile or above, hence many more thousands of schoolchildren at grade level or above.

1998-2001 SAT-9 Percent of all students scoring at or above the 50th percentile

Results of end of the year math testing on the California Standards Test in math are available to the public on the California Department of Education website. Grade level test results can be viewed by school, district, county and state. The results are disaggregated by ethnicity and socioeconomic status.

    Students who test at grade level or above are given a grade of “Proficient;” and if they do exceptionally well they are given a grade of “Advanced.”  Students who test below grade level are given a grade of “Basic,” “Below Basic” or “Far Below Basic” depending on how poorly they scored.  The chart linked here shows that from 2003 to 2008 there was a significant increase in the percentage of elementary and middle school students who tested Proficient and above on the California Standards Test in mathematics.

Percentages of Students Scoring at Proficient and Above*

*Data for 2003 through 2007 are final statewide results. The 2008 data are preliminary and include results for approximately 99% of the students in the states. Complete results will be available during September 2008. Percentages included in this table may differ from the percentages printed on the Internet reports due to rounding.

    There has also been a significant increase in the percentage of students who test at the Advanced level on the Standards Based Test in mathematics. The chart below shows the 2002-2008 increase in the percentage of fourth grade students who tested at the advanced level on the California Standards Test in mathematics. To see how other grade levels performed, link here.

More Low Income, Minority Students Are Improving and Achieving

     The state began end of the year math achievement testing in spring 1998 following adoption of math standards in December 1997.  The first test results indicated that there were low income, minority populated schools that tested higher in math achievement than middle class schools populated with White students. One of these schools was Bennett Kew in Inglewood, California where 86% of the third graders tested at the 50th percentile or above.

     Despite schools like Bennett Kew, there is still an achievement gap in the state. On average, low income, Hispanic and African American students do worse on end of the year math achievement testing than White and Asian students.

     However, there are many more schools like Bennett Kew, where low income, minority students do exceptionally well. Some are traditional public schools, others are magnets and charter schools.  Another example is Elysian Heights Elementary in Los Angeles where the school population is 84% Hispanic and 80% low socioeconomic.  Three quarters of the fourth graders tested Proficient and above on the California Standards Test in math in 2008. Thirty-nine percent of the fourth graders were at the Advanced level, and thirty-six percent were Proficient.  Fifteen percent were Basic, six percent were Below Basic and only three percent were Far Below Basic. At Richardson Prep, a magnet middle school in San Bernadino, 88% of the seventh graders tested at Proficient and above, the rest tested at Basic.  Richardson is about three quarters Hispanic and African American, and 64% low socioeconomic. 

     California schools need to replicate instructional programs that work and keep standards high for all students.  Every student in California deserves a standard of excellence, and by maintaining high standards, there can be equal opportunity for all.

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